ffirs.indd

Multiplication by 11 75
MULTIPLYING BY MULTIPLES OF 11
What are factors? We read about factors in Chapter 6. We found
that it is easy to multiply by 20 because 2 and 10 are factors of 20,
and it is easy to multiply by both 2 and 10.
It is easy to multiply by 22 because 22 is 2 times 11, and it is easy to
multiply by both 2 and 11.
It is easy to multiply by 33 because 33 is 3 times 11, and it is easy to
multiply by both 3 and 11.
Whenever you have to multiply any number by a multiple of 11—
such as 22 (2 × 11), 33 (3 × 11) or 44 (4 × 11)—you can combine
the use of factors and the shortcut for multiplication by 11. For
instance, if you want to multiply 16 by 22, it is easy if you see 22 as
2 × 11. Th en you multiply 16 by 2 to get 32, and use the shortcut
to multiply 32 by 11.
Let’s try multiplying 7 by 33.
7 × 3 = 21
21 × 11 = 2 31 Answer
How about multiplying 14 by 33? Th irty-three is 3 times 11. How
do you multiply 3 by 14? Fourteen has factors of 2 and 7. To multiply
3 × 14, you can multiply 3 × 2 × 7.
3 × 2 = 6
6 × 7 = 42
42 × 11 = 4 62 Answer
You can think of the problem 14 × 33 as 7 × 2 × 3 × 11. Seven
times 3 × 2 is the same as 7 × 6, which is 42. You are then left with
42 × 11. Teaching yourself to look for factors can make life easier
and can turn you into a real mathematician.